Properties

Label 400.2.y.c.209.1
Level $400$
Weight $2$
Character 400.209
Analytic conductor $3.194$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.y (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 209.1
Root \(1.66637 - 0.917186i\) of defining polynomial
Character \(\chi\) \(=\) 400.209
Dual form 400.2.y.c.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +O(q^{10})\) \(q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +(1.61803 + 1.17557i) q^{11} +(0.838893 + 1.15464i) q^{13} +(1.05361 - 0.132565i) q^{15} +(-1.76920 - 0.574848i) q^{17} +(0.279141 - 0.859107i) q^{19} +(0.445515 + 1.37116i) q^{21} +(1.95693 - 2.69348i) q^{23} +(4.64703 + 1.84529i) q^{25} +(-1.61189 + 2.21858i) q^{27} +(-1.22466 - 3.76910i) q^{29} +(1.99006 - 6.12477i) q^{31} +(0.903319 + 0.293506i) q^{33} +(-1.27534 + 6.66742i) q^{35} +(2.24547 + 3.09062i) q^{37} +(0.548341 + 0.398393i) q^{39} +(1.48391 - 1.07813i) q^{41} +3.59445i q^{43} +(-5.61478 + 2.63868i) q^{45} +(4.56502 - 1.48326i) q^{47} -2.21619 q^{49} -0.883436 q^{51} +(9.03953 - 2.93712i) q^{53} +(3.05975 + 3.26158i) q^{55} -0.428989i q^{57} +(-8.61248 + 6.25734i) q^{59} +(-11.5481 - 8.39016i) q^{61} +(-4.95078 - 6.81417i) q^{63} +(1.35736 + 2.88829i) q^{65} +(-10.1670 - 3.30345i) q^{67} +(0.488588 - 1.50372i) q^{69} +(-3.85030 - 11.8500i) q^{71} +(0.157310 - 0.216518i) q^{73} +(2.36968 + 0.151474i) q^{75} +(-3.56882 + 4.91206i) q^{77} +(-2.64882 - 8.15223i) q^{79} +(2.16963 - 6.67743i) q^{81} +(12.0006 + 3.89923i) q^{83} +(-3.64411 - 2.00575i) q^{85} +(-1.10626 - 1.52263i) q^{87} +(-3.85736 - 2.80253i) q^{89} +(-3.50527 + 2.54673i) q^{91} -3.05836i q^{93} +(0.973973 - 1.76955i) q^{95} +(-9.47067 + 3.07721i) q^{97} -5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.451659 0.146753i 0.260766 0.0847279i −0.175716 0.984441i \(-0.556224\pi\)
0.436482 + 0.899713i \(0.356224\pi\)
\(4\) 0 0
\(5\) 2.19625 + 0.420099i 0.982193 + 0.187874i
\(6\) 0 0
\(7\) 3.03582i 1.14743i 0.819055 + 0.573716i \(0.194498\pi\)
−0.819055 + 0.573716i \(0.805502\pi\)
\(8\) 0 0
\(9\) −2.24459 + 1.63079i −0.748197 + 0.543597i
\(10\) 0 0
\(11\) 1.61803 + 1.17557i 0.487856 + 0.354448i 0.804359 0.594144i \(-0.202509\pi\)
−0.316503 + 0.948591i \(0.602509\pi\)
\(12\) 0 0
\(13\) 0.838893 + 1.15464i 0.232667 + 0.320239i 0.909347 0.416039i \(-0.136582\pi\)
−0.676680 + 0.736277i \(0.736582\pi\)
\(14\) 0 0
\(15\) 1.05361 0.132565i 0.272040 0.0342281i
\(16\) 0 0
\(17\) −1.76920 0.574848i −0.429094 0.139421i 0.0865044 0.996251i \(-0.472430\pi\)
−0.515598 + 0.856830i \(0.672430\pi\)
\(18\) 0 0
\(19\) 0.279141 0.859107i 0.0640393 0.197093i −0.913918 0.405900i \(-0.866958\pi\)
0.977957 + 0.208807i \(0.0669581\pi\)
\(20\) 0 0
\(21\) 0.445515 + 1.37116i 0.0972194 + 0.299211i
\(22\) 0 0
\(23\) 1.95693 2.69348i 0.408048 0.561629i −0.554693 0.832055i \(-0.687164\pi\)
0.962741 + 0.270426i \(0.0871644\pi\)
\(24\) 0 0
\(25\) 4.64703 + 1.84529i 0.929407 + 0.369057i
\(26\) 0 0
\(27\) −1.61189 + 2.21858i −0.310208 + 0.426965i
\(28\) 0 0
\(29\) −1.22466 3.76910i −0.227413 0.699905i −0.998038 0.0626159i \(-0.980056\pi\)
0.770625 0.637289i \(-0.219944\pi\)
\(30\) 0 0
\(31\) 1.99006 6.12477i 0.357425 1.10004i −0.597165 0.802119i \(-0.703706\pi\)
0.954590 0.297923i \(-0.0962938\pi\)
\(32\) 0 0
\(33\) 0.903319 + 0.293506i 0.157248 + 0.0510929i
\(34\) 0 0
\(35\) −1.27534 + 6.66742i −0.215572 + 1.12700i
\(36\) 0 0
\(37\) 2.24547 + 3.09062i 0.369153 + 0.508095i 0.952670 0.304005i \(-0.0983241\pi\)
−0.583518 + 0.812100i \(0.698324\pi\)
\(38\) 0 0
\(39\) 0.548341 + 0.398393i 0.0878048 + 0.0637939i
\(40\) 0 0
\(41\) 1.48391 1.07813i 0.231749 0.168375i −0.465851 0.884863i \(-0.654252\pi\)
0.697599 + 0.716488i \(0.254252\pi\)
\(42\) 0 0
\(43\) 3.59445i 0.548149i 0.961708 + 0.274074i \(0.0883715\pi\)
−0.961708 + 0.274074i \(0.911629\pi\)
\(44\) 0 0
\(45\) −5.61478 + 2.63868i −0.837002 + 0.393350i
\(46\) 0 0
\(47\) 4.56502 1.48326i 0.665877 0.216356i 0.0434750 0.999055i \(-0.486157\pi\)
0.622402 + 0.782698i \(0.286157\pi\)
\(48\) 0 0
\(49\) −2.21619 −0.316598
\(50\) 0 0
\(51\) −0.883436 −0.123706
\(52\) 0 0
\(53\) 9.03953 2.93712i 1.24168 0.403445i 0.386745 0.922187i \(-0.373599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(54\) 0 0
\(55\) 3.05975 + 3.26158i 0.412577 + 0.439792i
\(56\) 0 0
\(57\) 0.428989i 0.0568209i
\(58\) 0 0
\(59\) −8.61248 + 6.25734i −1.12125 + 0.814636i −0.984398 0.175956i \(-0.943698\pi\)
−0.136852 + 0.990592i \(0.543698\pi\)
\(60\) 0 0
\(61\) −11.5481 8.39016i −1.47858 1.07425i −0.978012 0.208551i \(-0.933125\pi\)
−0.500566 0.865698i \(-0.666875\pi\)
\(62\) 0 0
\(63\) −4.95078 6.81417i −0.623740 0.858505i
\(64\) 0 0
\(65\) 1.35736 + 2.88829i 0.168359 + 0.358248i
\(66\) 0 0
\(67\) −10.1670 3.30345i −1.24209 0.403580i −0.387012 0.922075i \(-0.626493\pi\)
−0.855081 + 0.518494i \(0.826493\pi\)
\(68\) 0 0
\(69\) 0.488588 1.50372i 0.0588191 0.181027i
\(70\) 0 0
\(71\) −3.85030 11.8500i −0.456947 1.40634i −0.868834 0.495104i \(-0.835130\pi\)
0.411887 0.911235i \(-0.364870\pi\)
\(72\) 0 0
\(73\) 0.157310 0.216518i 0.0184117 0.0253415i −0.799712 0.600384i \(-0.795014\pi\)
0.818124 + 0.575042i \(0.195014\pi\)
\(74\) 0 0
\(75\) 2.36968 + 0.151474i 0.273627 + 0.0174907i
\(76\) 0 0
\(77\) −3.56882 + 4.91206i −0.406704 + 0.559781i
\(78\) 0 0
\(79\) −2.64882 8.15223i −0.298015 0.917197i −0.982192 0.187881i \(-0.939838\pi\)
0.684176 0.729316i \(-0.260162\pi\)
\(80\) 0 0
\(81\) 2.16963 6.67743i 0.241070 0.741937i
\(82\) 0 0
\(83\) 12.0006 + 3.89923i 1.31724 + 0.427996i 0.881545 0.472100i \(-0.156504\pi\)
0.435691 + 0.900096i \(0.356504\pi\)
\(84\) 0 0
\(85\) −3.64411 2.00575i −0.395260 0.217554i
\(86\) 0 0
\(87\) −1.10626 1.52263i −0.118603 0.163243i
\(88\) 0 0
\(89\) −3.85736 2.80253i −0.408879 0.297068i 0.364269 0.931294i \(-0.381319\pi\)
−0.773148 + 0.634226i \(0.781319\pi\)
\(90\) 0 0
\(91\) −3.50527 + 2.54673i −0.367452 + 0.266969i
\(92\) 0 0
\(93\) 3.05836i 0.317137i
\(94\) 0 0
\(95\) 0.973973 1.76955i 0.0999276 0.181552i
\(96\) 0 0
\(97\) −9.47067 + 3.07721i −0.961600 + 0.312443i −0.747420 0.664351i \(-0.768708\pi\)
−0.214180 + 0.976794i \(0.568708\pi\)
\(98\) 0 0
\(99\) −5.54893 −0.557689
\(100\) 0 0
\(101\) 9.34612 0.929974 0.464987 0.885318i \(-0.346059\pi\)
0.464987 + 0.885318i \(0.346059\pi\)
\(102\) 0 0
\(103\) 8.63947 2.80713i 0.851272 0.276595i 0.149294 0.988793i \(-0.452300\pi\)
0.701979 + 0.712198i \(0.252300\pi\)
\(104\) 0 0
\(105\) 0.402443 + 3.19856i 0.0392744 + 0.312148i
\(106\) 0 0
\(107\) 5.62871i 0.544148i 0.962276 + 0.272074i \(0.0877096\pi\)
−0.962276 + 0.272074i \(0.912290\pi\)
\(108\) 0 0
\(109\) −8.18158 + 5.94427i −0.783654 + 0.569358i −0.906073 0.423121i \(-0.860935\pi\)
0.122420 + 0.992478i \(0.460935\pi\)
\(110\) 0 0
\(111\) 1.46774 + 1.06638i 0.139312 + 0.101216i
\(112\) 0 0
\(113\) −6.29636 8.66620i −0.592312 0.815247i 0.402666 0.915347i \(-0.368084\pi\)
−0.994977 + 0.100100i \(0.968084\pi\)
\(114\) 0 0
\(115\) 5.42943 5.09345i 0.506297 0.474967i
\(116\) 0 0
\(117\) −3.76594 1.22363i −0.348162 0.113125i
\(118\) 0 0
\(119\) 1.74513 5.37097i 0.159976 0.492356i
\(120\) 0 0
\(121\) −2.16312 6.65740i −0.196647 0.605218i
\(122\) 0 0
\(123\) 0.512006 0.704715i 0.0461660 0.0635420i
\(124\) 0 0
\(125\) 9.43085 + 6.00492i 0.843521 + 0.537097i
\(126\) 0 0
\(127\) −6.67779 + 9.19118i −0.592558 + 0.815586i −0.995002 0.0998589i \(-0.968161\pi\)
0.402444 + 0.915445i \(0.368161\pi\)
\(128\) 0 0
\(129\) 0.527497 + 1.62347i 0.0464435 + 0.142938i
\(130\) 0 0
\(131\) −2.46834 + 7.59677i −0.215660 + 0.663732i 0.783446 + 0.621459i \(0.213460\pi\)
−0.999106 + 0.0422730i \(0.986540\pi\)
\(132\) 0 0
\(133\) 2.60809 + 0.847421i 0.226150 + 0.0734807i
\(134\) 0 0
\(135\) −4.47214 + 4.19540i −0.384900 + 0.361082i
\(136\) 0 0
\(137\) 5.48831 + 7.55401i 0.468898 + 0.645382i 0.976324 0.216313i \(-0.0694031\pi\)
−0.507426 + 0.861695i \(0.669403\pi\)
\(138\) 0 0
\(139\) −14.4936 10.5302i −1.22933 0.893160i −0.232489 0.972599i \(-0.574687\pi\)
−0.996840 + 0.0794393i \(0.974687\pi\)
\(140\) 0 0
\(141\) 1.84416 1.33986i 0.155306 0.112837i
\(142\) 0 0
\(143\) 2.85442i 0.238699i
\(144\) 0 0
\(145\) −1.10626 8.79238i −0.0918695 0.730167i
\(146\) 0 0
\(147\) −1.00096 + 0.325232i −0.0825579 + 0.0268247i
\(148\) 0 0
\(149\) 6.31395 0.517259 0.258629 0.965977i \(-0.416729\pi\)
0.258629 + 0.965977i \(0.416729\pi\)
\(150\) 0 0
\(151\) −4.71947 −0.384065 −0.192033 0.981389i \(-0.561508\pi\)
−0.192033 + 0.981389i \(0.561508\pi\)
\(152\) 0 0
\(153\) 4.90859 1.59490i 0.396836 0.128940i
\(154\) 0 0
\(155\) 6.94368 12.6155i 0.557730 1.01330i
\(156\) 0 0
\(157\) 1.46908i 0.117245i −0.998280 0.0586225i \(-0.981329\pi\)
0.998280 0.0586225i \(-0.0186708\pi\)
\(158\) 0 0
\(159\) 3.65176 2.65316i 0.289603 0.210409i
\(160\) 0 0
\(161\) 8.17691 + 5.94087i 0.644431 + 0.468206i
\(162\) 0 0
\(163\) 2.62134 + 3.60797i 0.205319 + 0.282598i 0.899242 0.437452i \(-0.144119\pi\)
−0.693922 + 0.720050i \(0.744119\pi\)
\(164\) 0 0
\(165\) 1.86061 + 1.02410i 0.144849 + 0.0797258i
\(166\) 0 0
\(167\) 9.92300 + 3.22418i 0.767865 + 0.249494i 0.666651 0.745370i \(-0.267727\pi\)
0.101214 + 0.994865i \(0.467727\pi\)
\(168\) 0 0
\(169\) 3.38778 10.4265i 0.260598 0.802038i
\(170\) 0 0
\(171\) 0.774467 + 2.38357i 0.0592250 + 0.182276i
\(172\) 0 0
\(173\) −4.51195 + 6.21017i −0.343037 + 0.472151i −0.945326 0.326128i \(-0.894256\pi\)
0.602288 + 0.798279i \(0.294256\pi\)
\(174\) 0 0
\(175\) −5.60195 + 14.1075i −0.423468 + 1.06643i
\(176\) 0 0
\(177\) −2.97163 + 4.09009i −0.223361 + 0.307430i
\(178\) 0 0
\(179\) 4.79494 + 14.7573i 0.358391 + 1.10301i 0.954017 + 0.299752i \(0.0969040\pi\)
−0.595626 + 0.803262i \(0.703096\pi\)
\(180\) 0 0
\(181\) −0.491509 + 1.51271i −0.0365336 + 0.112439i −0.967660 0.252257i \(-0.918827\pi\)
0.931127 + 0.364696i \(0.118827\pi\)
\(182\) 0 0
\(183\) −6.44707 2.09478i −0.476581 0.154851i
\(184\) 0 0
\(185\) 3.63324 + 7.73110i 0.267121 + 0.568402i
\(186\) 0 0
\(187\) −2.18685 3.00994i −0.159918 0.220109i
\(188\) 0 0
\(189\) −6.73519 4.89340i −0.489913 0.355943i
\(190\) 0 0
\(191\) 15.9121 11.5608i 1.15136 0.836511i 0.162698 0.986676i \(-0.447980\pi\)
0.988661 + 0.150164i \(0.0479803\pi\)
\(192\) 0 0
\(193\) 13.1100i 0.943680i 0.881684 + 0.471840i \(0.156410\pi\)
−0.881684 + 0.471840i \(0.843590\pi\)
\(194\) 0 0
\(195\) 1.03693 + 1.10533i 0.0742560 + 0.0791542i
\(196\) 0 0
\(197\) −3.26164 + 1.05977i −0.232382 + 0.0755055i −0.422893 0.906180i \(-0.638985\pi\)
0.190511 + 0.981685i \(0.438985\pi\)
\(198\) 0 0
\(199\) 17.6959 1.25443 0.627215 0.778846i \(-0.284195\pi\)
0.627215 + 0.778846i \(0.284195\pi\)
\(200\) 0 0
\(201\) −5.07680 −0.358090
\(202\) 0 0
\(203\) 11.4423 3.71783i 0.803093 0.260941i
\(204\) 0 0
\(205\) 3.71197 1.74445i 0.259255 0.121837i
\(206\) 0 0
\(207\) 9.23710i 0.642023i
\(208\) 0 0
\(209\) 1.46160 1.06192i 0.101101 0.0734542i
\(210\) 0 0
\(211\) −2.62418 1.90658i −0.180656 0.131254i 0.493782 0.869586i \(-0.335614\pi\)
−0.674438 + 0.738331i \(0.735614\pi\)
\(212\) 0 0
\(213\) −3.47805 4.78713i −0.238312 0.328009i
\(214\) 0 0
\(215\) −1.51003 + 7.89432i −0.102983 + 0.538388i
\(216\) 0 0
\(217\) 18.5937 + 6.04145i 1.26222 + 0.410121i
\(218\) 0 0
\(219\) 0.0392757 0.120878i 0.00265401 0.00816819i
\(220\) 0 0
\(221\) −0.820429 2.52502i −0.0551880 0.169851i
\(222\) 0 0
\(223\) −16.8781 + 23.2307i −1.13024 + 1.55564i −0.342633 + 0.939469i \(0.611319\pi\)
−0.787609 + 0.616175i \(0.788681\pi\)
\(224\) 0 0
\(225\) −13.4400 + 3.43643i −0.895998 + 0.229095i
\(226\) 0 0
\(227\) 6.88921 9.48219i 0.457253 0.629355i −0.516683 0.856177i \(-0.672833\pi\)
0.973936 + 0.226822i \(0.0728335\pi\)
\(228\) 0 0
\(229\) 5.06828 + 15.5985i 0.334921 + 1.03078i 0.966761 + 0.255682i \(0.0823000\pi\)
−0.631840 + 0.775099i \(0.717700\pi\)
\(230\) 0 0
\(231\) −0.891031 + 2.74231i −0.0586255 + 0.180431i
\(232\) 0 0
\(233\) 21.4126 + 6.95739i 1.40279 + 0.455794i 0.910092 0.414407i \(-0.136011\pi\)
0.492697 + 0.870201i \(0.336011\pi\)
\(234\) 0 0
\(235\) 10.6490 1.33986i 0.694667 0.0874029i
\(236\) 0 0
\(237\) −2.39273 3.29331i −0.155424 0.213923i
\(238\) 0 0
\(239\) 5.36647 + 3.89897i 0.347128 + 0.252204i 0.747663 0.664078i \(-0.231176\pi\)
−0.400535 + 0.916281i \(0.631176\pi\)
\(240\) 0 0
\(241\) −21.2173 + 15.4153i −1.36673 + 0.992986i −0.368743 + 0.929531i \(0.620212\pi\)
−0.997985 + 0.0634545i \(0.979788\pi\)
\(242\) 0 0
\(243\) 11.5613i 0.741655i
\(244\) 0 0
\(245\) −4.86730 0.931017i −0.310960 0.0594805i
\(246\) 0 0
\(247\) 1.22613 0.398393i 0.0780166 0.0253491i
\(248\) 0 0
\(249\) 5.99241 0.379753
\(250\) 0 0
\(251\) 10.9121 0.688766 0.344383 0.938829i \(-0.388088\pi\)
0.344383 + 0.938829i \(0.388088\pi\)
\(252\) 0 0
\(253\) 6.33275 2.05763i 0.398137 0.129362i
\(254\) 0 0
\(255\) −1.94025 0.371131i −0.121503 0.0232411i
\(256\) 0 0
\(257\) 6.58051i 0.410481i −0.978712 0.205240i \(-0.934202\pi\)
0.978712 0.205240i \(-0.0657976\pi\)
\(258\) 0 0
\(259\) −9.38256 + 6.81683i −0.583004 + 0.423577i
\(260\) 0 0
\(261\) 8.89547 + 6.46294i 0.550616 + 0.400046i
\(262\) 0 0
\(263\) −15.9332 21.9302i −0.982486 1.35228i −0.935479 0.353382i \(-0.885032\pi\)
−0.0470069 0.998895i \(-0.514968\pi\)
\(264\) 0 0
\(265\) 21.0870 2.65316i 1.29536 0.162982i
\(266\) 0 0
\(267\) −2.15349 0.699712i −0.131792 0.0428217i
\(268\) 0 0
\(269\) −0.311938 + 0.960046i −0.0190192 + 0.0585350i −0.960116 0.279603i \(-0.909797\pi\)
0.941096 + 0.338138i \(0.109797\pi\)
\(270\) 0 0
\(271\) −1.93198 5.94603i −0.117360 0.361196i 0.875072 0.483992i \(-0.160814\pi\)
−0.992432 + 0.122796i \(0.960814\pi\)
\(272\) 0 0
\(273\) −1.20945 + 1.66466i −0.0731991 + 0.100750i
\(274\) 0 0
\(275\) 5.34980 + 8.44865i 0.322605 + 0.509473i
\(276\) 0 0
\(277\) 14.5009 19.9587i 0.871272 1.19920i −0.107491 0.994206i \(-0.534282\pi\)
0.978763 0.204997i \(-0.0657184\pi\)
\(278\) 0 0
\(279\) 5.52135 + 16.9930i 0.330555 + 1.01734i
\(280\) 0 0
\(281\) 0.568255 1.74891i 0.0338993 0.104331i −0.932675 0.360717i \(-0.882532\pi\)
0.966574 + 0.256386i \(0.0825319\pi\)
\(282\) 0 0
\(283\) 8.21823 + 2.67026i 0.488523 + 0.158731i 0.542913 0.839789i \(-0.317321\pi\)
−0.0543898 + 0.998520i \(0.517321\pi\)
\(284\) 0 0
\(285\) 0.180218 0.942167i 0.0106752 0.0558091i
\(286\) 0 0
\(287\) 3.27300 + 4.50489i 0.193199 + 0.265915i
\(288\) 0 0
\(289\) −10.9537 7.95831i −0.644334 0.468136i
\(290\) 0 0
\(291\) −3.82593 + 2.77970i −0.224280 + 0.162949i
\(292\) 0 0
\(293\) 6.29156i 0.367557i 0.982968 + 0.183779i \(0.0588329\pi\)
−0.982968 + 0.183779i \(0.941167\pi\)
\(294\) 0 0
\(295\) −21.5439 + 10.1246i −1.25433 + 0.589476i
\(296\) 0 0
\(297\) −5.21619 + 1.69484i −0.302674 + 0.0983447i
\(298\) 0 0
\(299\) 4.75164 0.274795
\(300\) 0 0
\(301\) −10.9121 −0.628963
\(302\) 0 0
\(303\) 4.22126 1.37157i 0.242505 0.0787947i
\(304\) 0 0
\(305\) −21.8377 23.2782i −1.25043 1.33291i
\(306\) 0 0
\(307\) 28.6661i 1.63606i −0.575175 0.818030i \(-0.695066\pi\)
0.575175 0.818030i \(-0.304934\pi\)
\(308\) 0 0
\(309\) 3.49014 2.53574i 0.198547 0.144253i
\(310\) 0 0
\(311\) −6.33985 4.60617i −0.359500 0.261192i 0.393343 0.919392i \(-0.371318\pi\)
−0.752844 + 0.658199i \(0.771318\pi\)
\(312\) 0 0
\(313\) −12.5840 17.3205i −0.711292 0.979010i −0.999768 0.0215228i \(-0.993149\pi\)
0.288476 0.957487i \(-0.406851\pi\)
\(314\) 0 0
\(315\) −8.01054 17.0454i −0.451343 0.960402i
\(316\) 0 0
\(317\) −3.82309 1.24220i −0.214726 0.0697688i 0.199679 0.979861i \(-0.436010\pi\)
−0.414405 + 0.910093i \(0.636010\pi\)
\(318\) 0 0
\(319\) 2.44931 7.53821i 0.137135 0.422059i
\(320\) 0 0
\(321\) 0.826031 + 2.54226i 0.0461046 + 0.141895i
\(322\) 0 0
\(323\) −0.987712 + 1.35947i −0.0549578 + 0.0756429i
\(324\) 0 0
\(325\) 1.76773 + 6.91364i 0.0980560 + 0.383499i
\(326\) 0 0
\(327\) −2.82295 + 3.88546i −0.156109 + 0.214866i
\(328\) 0 0
\(329\) 4.50292 + 13.8586i 0.248254 + 0.764047i
\(330\) 0 0
\(331\) −3.59815 + 11.0740i −0.197772 + 0.608681i 0.802161 + 0.597108i \(0.203684\pi\)
−0.999933 + 0.0115724i \(0.996316\pi\)
\(332\) 0 0
\(333\) −10.0803 3.27529i −0.552398 0.179485i
\(334\) 0 0
\(335\) −20.9414 11.5263i −1.14415 0.629751i
\(336\) 0 0
\(337\) −12.6578 17.4220i −0.689516 0.949037i 0.310483 0.950579i \(-0.399509\pi\)
−0.999999 + 0.00154181i \(0.999509\pi\)
\(338\) 0 0
\(339\) −4.11560 2.99016i −0.223529 0.162403i
\(340\) 0 0
\(341\) 10.4201 7.57063i 0.564279 0.409973i
\(342\) 0 0
\(343\) 14.5228i 0.784157i
\(344\) 0 0
\(345\) 1.70477 3.09729i 0.0917819 0.166753i
\(346\) 0 0
\(347\) −14.8339 + 4.81981i −0.796323 + 0.258741i −0.678794 0.734328i \(-0.737497\pi\)
−0.117529 + 0.993069i \(0.537497\pi\)
\(348\) 0 0
\(349\) −5.56598 −0.297940 −0.148970 0.988842i \(-0.547596\pi\)
−0.148970 + 0.988842i \(0.547596\pi\)
\(350\) 0 0
\(351\) −3.91385 −0.208906
\(352\) 0 0
\(353\) −7.62953 + 2.47898i −0.406079 + 0.131943i −0.504932 0.863159i \(-0.668483\pi\)
0.0988533 + 0.995102i \(0.468483\pi\)
\(354\) 0 0
\(355\) −3.47805 27.6431i −0.184596 1.46714i
\(356\) 0 0
\(357\) 2.68195i 0.141944i
\(358\) 0 0
\(359\) 9.98547 7.25487i 0.527013 0.382897i −0.292226 0.956349i \(-0.594396\pi\)
0.819239 + 0.573452i \(0.194396\pi\)
\(360\) 0 0
\(361\) 14.7112 + 10.6883i 0.774272 + 0.562542i
\(362\) 0 0
\(363\) −1.95399 2.68943i −0.102558 0.141159i
\(364\) 0 0
\(365\) 0.436451 0.409443i 0.0228449 0.0214312i
\(366\) 0 0
\(367\) 25.5596 + 8.30481i 1.33420 + 0.433508i 0.887348 0.461100i \(-0.152545\pi\)
0.446852 + 0.894608i \(0.352545\pi\)
\(368\) 0 0
\(369\) −1.57258 + 4.83991i −0.0818653 + 0.251956i
\(370\) 0 0
\(371\) 8.91657 + 27.4424i 0.462925 + 1.42474i
\(372\) 0 0
\(373\) −16.2457 + 22.3604i −0.841173 + 1.15778i 0.144566 + 0.989495i \(0.453821\pi\)
−0.985739 + 0.168280i \(0.946179\pi\)
\(374\) 0 0
\(375\) 5.14077 + 1.32817i 0.265468 + 0.0685866i
\(376\) 0 0
\(377\) 3.32459 4.57591i 0.171225 0.235671i
\(378\) 0 0
\(379\) −1.07372 3.30456i −0.0551532 0.169744i 0.919685 0.392656i \(-0.128444\pi\)
−0.974839 + 0.222912i \(0.928444\pi\)
\(380\) 0 0
\(381\) −1.66725 + 5.13127i −0.0854159 + 0.262883i
\(382\) 0 0
\(383\) −26.0322 8.45837i −1.33018 0.432203i −0.444203 0.895926i \(-0.646513\pi\)
−0.885980 + 0.463723i \(0.846513\pi\)
\(384\) 0 0
\(385\) −9.90157 + 9.28885i −0.504631 + 0.473404i
\(386\) 0 0
\(387\) −5.86180 8.06808i −0.297972 0.410123i
\(388\) 0 0
\(389\) 8.80576 + 6.39776i 0.446470 + 0.324379i 0.788200 0.615419i \(-0.211013\pi\)
−0.341731 + 0.939798i \(0.611013\pi\)
\(390\) 0 0
\(391\) −5.01054 + 3.64037i −0.253394 + 0.184101i
\(392\) 0 0
\(393\) 3.79339i 0.191351i
\(394\) 0 0
\(395\) −2.39273 19.0171i −0.120391 0.956854i
\(396\) 0 0
\(397\) 15.4273 5.01264i 0.774275 0.251577i 0.104881 0.994485i \(-0.466554\pi\)
0.669394 + 0.742908i \(0.266554\pi\)
\(398\) 0 0
\(399\) 1.30233 0.0651981
\(400\) 0 0
\(401\) 3.78686 0.189107 0.0945534 0.995520i \(-0.469858\pi\)
0.0945534 + 0.995520i \(0.469858\pi\)
\(402\) 0 0
\(403\) 8.74134 2.84023i 0.435437 0.141482i
\(404\) 0 0
\(405\) 7.57024 13.7539i 0.376168 0.683435i
\(406\) 0 0
\(407\) 7.64044i 0.378722i
\(408\) 0 0
\(409\) 1.50142 1.09084i 0.0742403 0.0539388i −0.550046 0.835134i \(-0.685390\pi\)
0.624286 + 0.781196i \(0.285390\pi\)
\(410\) 0 0
\(411\) 3.58742 + 2.60641i 0.176954 + 0.128565i
\(412\) 0 0
\(413\) −18.9961 26.1459i −0.934738 1.28656i
\(414\) 0 0
\(415\) 24.7182 + 13.6051i 1.21337 + 0.667849i
\(416\) 0 0
\(417\) −8.09150 2.62909i −0.396242 0.128747i
\(418\) 0 0
\(419\) 4.43353 13.6450i 0.216592 0.666602i −0.782445 0.622720i \(-0.786028\pi\)
0.999037 0.0438818i \(-0.0139725\pi\)
\(420\) 0 0
\(421\) 4.77571 + 14.6981i 0.232754 + 0.716343i 0.997411 + 0.0719060i \(0.0229082\pi\)
−0.764658 + 0.644437i \(0.777092\pi\)
\(422\) 0 0
\(423\) −7.82771 + 10.7739i −0.380596 + 0.523846i
\(424\) 0 0
\(425\) −7.16077 5.93602i −0.347348 0.287939i
\(426\) 0 0
\(427\) 25.4710 35.0578i 1.23263 1.69657i
\(428\) 0 0
\(429\) 0.418895 + 1.28923i 0.0202244 + 0.0622444i
\(430\) 0 0
\(431\) −3.86404 + 11.8923i −0.186124 + 0.572832i −0.999966 0.00825486i \(-0.997372\pi\)
0.813842 + 0.581087i \(0.197372\pi\)
\(432\) 0 0
\(433\) −21.3941 6.95138i −1.02814 0.334062i −0.254084 0.967182i \(-0.581774\pi\)
−0.774053 + 0.633120i \(0.781774\pi\)
\(434\) 0 0
\(435\) −1.78996 3.80881i −0.0858219 0.182619i
\(436\) 0 0
\(437\) −1.76773 2.43307i −0.0845620 0.116390i
\(438\) 0 0
\(439\) −9.85186 7.15780i −0.470204 0.341623i 0.327317 0.944915i \(-0.393855\pi\)
−0.797521 + 0.603292i \(0.793855\pi\)
\(440\) 0 0
\(441\) 4.97443 3.61414i 0.236878 0.172102i
\(442\) 0 0
\(443\) 20.7101i 0.983968i 0.870604 + 0.491984i \(0.163728\pi\)
−0.870604 + 0.491984i \(0.836272\pi\)
\(444\) 0 0
\(445\) −7.29438 7.77554i −0.345787 0.368596i
\(446\) 0 0
\(447\) 2.85176 0.926591i 0.134883 0.0438263i
\(448\) 0 0
\(449\) 25.9539 1.22484 0.612420 0.790533i \(-0.290196\pi\)
0.612420 + 0.790533i \(0.290196\pi\)
\(450\) 0 0
\(451\) 3.66844 0.172740
\(452\) 0 0
\(453\) −2.13159 + 0.692597i −0.100151 + 0.0325411i
\(454\) 0 0
\(455\) −8.76832 + 4.12069i −0.411065 + 0.193181i
\(456\) 0 0
\(457\) 8.50150i 0.397684i 0.980032 + 0.198842i \(0.0637180\pi\)
−0.980032 + 0.198842i \(0.936282\pi\)
\(458\) 0 0
\(459\) 4.12710 2.99851i 0.192636 0.139959i
\(460\) 0 0
\(461\) −11.9614 8.69044i −0.557097 0.404754i 0.273299 0.961929i \(-0.411885\pi\)
−0.830395 + 0.557175i \(0.811885\pi\)
\(462\) 0 0
\(463\) −13.0442 17.9538i −0.606215 0.834384i 0.390044 0.920796i \(-0.372460\pi\)
−0.996259 + 0.0864125i \(0.972460\pi\)
\(464\) 0 0
\(465\) 1.28481 6.71692i 0.0595818 0.311490i
\(466\) 0 0
\(467\) −27.1064 8.80741i −1.25434 0.407558i −0.394863 0.918740i \(-0.629208\pi\)
−0.859473 + 0.511182i \(0.829208\pi\)
\(468\) 0 0
\(469\) 10.0287 30.8651i 0.463081 1.42522i
\(470\) 0 0
\(471\) −0.215591 0.663522i −0.00993393 0.0305735i
\(472\) 0 0
\(473\) −4.22553 + 5.81595i −0.194290 + 0.267418i
\(474\) 0 0
\(475\) 2.88248 3.47721i 0.132257 0.159545i
\(476\) 0 0
\(477\) −15.5002 + 21.3342i −0.709707 + 0.976827i
\(478\) 0 0
\(479\) 7.74301 + 23.8305i 0.353787 + 1.08885i 0.956709 + 0.291045i \(0.0940030\pi\)
−0.602922 + 0.797800i \(0.705997\pi\)
\(480\) 0 0
\(481\) −1.68484 + 5.18540i −0.0768220 + 0.236434i
\(482\) 0 0
\(483\) 4.56502 + 1.48326i 0.207716 + 0.0674909i
\(484\) 0 0
\(485\) −22.0927 + 2.77970i −1.00318 + 0.126220i
\(486\) 0 0
\(487\) 0.860980 + 1.18504i 0.0390147 + 0.0536992i 0.828079 0.560612i \(-0.189434\pi\)
−0.789064 + 0.614311i \(0.789434\pi\)
\(488\) 0 0
\(489\) 1.71343 + 1.24488i 0.0774842 + 0.0562955i
\(490\) 0 0
\(491\) −16.2359 + 11.7961i −0.732715 + 0.532348i −0.890421 0.455138i \(-0.849590\pi\)
0.157706 + 0.987486i \(0.449590\pi\)
\(492\) 0 0
\(493\) 7.37229i 0.332031i
\(494\) 0 0
\(495\) −12.1869 2.33110i −0.547758 0.104775i
\(496\) 0 0
\(497\) 35.9745 11.6888i 1.61368 0.524315i
\(498\) 0 0
\(499\) 0.624999 0.0279788 0.0139894 0.999902i \(-0.495547\pi\)
0.0139894 + 0.999902i \(0.495547\pi\)
\(500\) 0 0
\(501\) 4.95498 0.221372
\(502\) 0 0
\(503\) −18.3603 + 5.96563i −0.818647 + 0.265994i −0.688256 0.725468i \(-0.741623\pi\)
−0.130391 + 0.991463i \(0.541623\pi\)
\(504\) 0 0
\(505\) 20.5264 + 3.92630i 0.913414 + 0.174718i
\(506\) 0 0
\(507\) 5.20639i 0.231224i
\(508\) 0 0
\(509\) −8.51099 + 6.18360i −0.377243 + 0.274083i −0.760208 0.649680i \(-0.774903\pi\)
0.382965 + 0.923763i \(0.374903\pi\)
\(510\) 0 0
\(511\) 0.657310 + 0.477563i 0.0290777 + 0.0211262i
\(512\) 0 0
\(513\) 1.45605 + 2.00408i 0.0642862 + 0.0884824i
\(514\) 0 0
\(515\) 20.1537 2.53574i 0.888079 0.111738i
\(516\) 0 0
\(517\) 9.13004 + 2.96653i 0.401539 + 0.130468i
\(518\) 0 0
\(519\) −1.12650 + 3.46703i −0.0494481 + 0.152186i
\(520\) 0 0
\(521\) −3.09232 9.51719i −0.135477 0.416956i 0.860187 0.509979i \(-0.170347\pi\)
−0.995664 + 0.0930234i \(0.970347\pi\)
\(522\) 0 0
\(523\) −13.3915 + 18.4319i −0.585571 + 0.805970i −0.994292 0.106690i \(-0.965975\pi\)
0.408721 + 0.912659i \(0.365975\pi\)
\(524\) 0 0
\(525\) −0.459848 + 7.19391i −0.0200694 + 0.313968i
\(526\) 0 0
\(527\) −7.04162 + 9.69196i −0.306738 + 0.422188i
\(528\) 0 0
\(529\) 3.68213 + 11.3324i 0.160092 + 0.492714i
\(530\) 0 0
\(531\) 9.12710 28.0903i 0.396082 1.21902i
\(532\) 0 0
\(533\) 2.48969 + 0.808950i 0.107841 + 0.0350395i
\(534\) 0 0
\(535\) −2.36462 + 12.3621i −0.102231 + 0.534459i
\(536\) 0 0
\(537\) 4.33136 + 5.96161i 0.186912 + 0.257262i
\(538\) 0 0
\(539\) −3.58586 2.60528i −0.154454 0.112217i
\(540\) 0 0
\(541\) −2.63658 + 1.91559i −0.113356 + 0.0823576i −0.643019 0.765850i \(-0.722318\pi\)
0.529663 + 0.848208i \(0.322318\pi\)
\(542\) 0 0
\(543\) 0.755360i 0.0324156i
\(544\) 0 0
\(545\) −20.4660 + 9.61803i −0.876667 + 0.411991i
\(546\) 0 0
\(547\) 12.9232 4.19901i 0.552557 0.179537i −0.0194122 0.999812i \(-0.506179\pi\)
0.571970 + 0.820275i \(0.306179\pi\)
\(548\) 0 0
\(549\) 39.6033 1.69023
\(550\) 0 0
\(551\) −3.57992 −0.152510
\(552\) 0 0
\(553\) 24.7487 8.04133i 1.05242 0.341952i
\(554\) 0 0
\(555\) 2.77555 + 2.95863i 0.117816 + 0.125587i
\(556\) 0 0
\(557\) 27.6399i 1.17114i 0.810621 + 0.585571i \(0.199130\pi\)
−0.810621 + 0.585571i \(0.800870\pi\)
\(558\) 0 0
\(559\) −4.15029 + 3.01536i −0.175539 + 0.127536i
\(560\) 0 0
\(561\) −1.42943 1.03854i −0.0603506 0.0438473i
\(562\) 0 0
\(563\) −0.975284 1.34236i −0.0411033 0.0565738i 0.787971 0.615713i \(-0.211132\pi\)
−0.829074 + 0.559139i \(0.811132\pi\)
\(564\) 0 0
\(565\) −10.1877 21.6782i −0.428601 0.912010i
\(566\) 0 0
\(567\) 20.2715 + 6.58660i 0.851322 + 0.276611i
\(568\) 0 0
\(569\) −5.52609 + 17.0076i −0.231666 + 0.712994i 0.765880 + 0.642983i \(0.222303\pi\)
−0.997546 + 0.0700110i \(0.977697\pi\)
\(570\) 0 0
\(571\) 11.3942 + 35.0677i 0.476832 + 1.46754i 0.843472 + 0.537174i \(0.180508\pi\)
−0.366640 + 0.930363i \(0.619492\pi\)
\(572\) 0 0
\(573\) 5.49027 7.55670i 0.229359 0.315686i
\(574\) 0 0
\(575\) 14.0641 8.90560i 0.586515 0.371389i
\(576\) 0 0
\(577\) 13.4095 18.4567i 0.558247 0.768361i −0.432855 0.901463i \(-0.642494\pi\)
0.991102 + 0.133103i \(0.0424940\pi\)
\(578\) 0 0
\(579\) 1.92394 + 5.92127i 0.0799560 + 0.246079i
\(580\) 0 0
\(581\) −11.8373 + 36.4316i −0.491096 + 1.51144i
\(582\) 0 0
\(583\) 18.0791 + 5.87425i 0.748759 + 0.243286i
\(584\) 0 0
\(585\) −7.75691 4.26947i −0.320709 0.176521i
\(586\) 0 0
\(587\) 6.51588 + 8.96834i 0.268939 + 0.370163i 0.922031 0.387116i \(-0.126529\pi\)
−0.653092 + 0.757278i \(0.726529\pi\)
\(588\) 0 0
\(589\) −4.70633 3.41935i −0.193921 0.140892i
\(590\) 0 0
\(591\) −1.31762 + 0.957311i −0.0541998 + 0.0393785i
\(592\) 0 0
\(593\) 11.1321i 0.457139i 0.973528 + 0.228570i \(0.0734049\pi\)
−0.973528 + 0.228570i \(0.926595\pi\)
\(594\) 0 0
\(595\) 6.08909 11.0629i 0.249628 0.453533i
\(596\) 0 0
\(597\) 7.99253 2.59693i 0.327112 0.106285i
\(598\) 0 0
\(599\) 36.2736 1.48210 0.741049 0.671451i \(-0.234329\pi\)
0.741049 + 0.671451i \(0.234329\pi\)
\(600\) 0 0
\(601\) −15.1051 −0.616150 −0.308075 0.951362i \(-0.599685\pi\)
−0.308075 + 0.951362i \(0.599685\pi\)
\(602\) 0 0
\(603\) 28.2079 9.16531i 1.14872 0.373240i
\(604\) 0 0
\(605\) −1.95399 15.5300i −0.0794408 0.631386i
\(606\) 0 0
\(607\) 33.5066i 1.35999i −0.733216 0.679996i \(-0.761982\pi\)
0.733216 0.679996i \(-0.238018\pi\)
\(608\) 0 0
\(609\) 4.62243 3.35839i 0.187310 0.136089i
\(610\) 0 0
\(611\) 5.54220 + 4.02664i 0.224213 + 0.162900i
\(612\) 0 0
\(613\) 16.4750 + 22.6758i 0.665418 + 0.915869i 0.999646 0.0266235i \(-0.00847552\pi\)
−0.334228 + 0.942492i \(0.608476\pi\)
\(614\) 0 0
\(615\) 1.42054 1.33264i 0.0572818 0.0537372i
\(616\) 0 0
\(617\) −29.0284 9.43191i −1.16864 0.379714i −0.340505 0.940243i \(-0.610598\pi\)
−0.828135 + 0.560528i \(0.810598\pi\)
\(618\) 0 0
\(619\) −6.70477 + 20.6352i −0.269488 + 0.829398i 0.721138 + 0.692792i \(0.243619\pi\)
−0.990625 + 0.136606i \(0.956381\pi\)
\(620\) 0 0
\(621\) 2.82134 + 8.68318i 0.113216 + 0.348444i
\(622\) 0 0
\(623\) 8.50798 11.7102i 0.340865 0.469161i
\(624\) 0 0
\(625\) 18.1898 + 17.1502i 0.727594 + 0.686008i
\(626\) 0 0
\(627\) 0.504306 0.694118i 0.0201401 0.0277204i
\(628\) 0 0
\(629\) −2.19604 6.75873i −0.0875620 0.269488i
\(630\) 0 0
\(631\) 5.01463 15.4335i 0.199629 0.614396i −0.800262 0.599651i \(-0.795306\pi\)
0.999891 0.0147456i \(-0.00469383\pi\)
\(632\) 0 0
\(633\) −1.46503 0.476017i −0.0582297 0.0189200i
\(634\) 0 0
\(635\) −18.5273 + 17.3808i −0.735233 + 0.689737i
\(636\) 0 0
\(637\) −1.85914 2.55889i −0.0736619 0.101387i
\(638\) 0 0
\(639\) 27.9673 + 20.3194i 1.10637 + 0.803823i
\(640\) 0 0
\(641\) 17.9419 13.0356i 0.708663 0.514874i −0.174079 0.984732i \(-0.555695\pi\)
0.882742 + 0.469858i \(0.155695\pi\)
\(642\) 0 0
\(643\) 13.2767i 0.523583i 0.965124 + 0.261792i \(0.0843133\pi\)
−0.965124 + 0.261792i \(0.915687\pi\)
\(644\) 0 0
\(645\) 0.476498 + 3.78714i 0.0187621 + 0.149119i
\(646\) 0 0
\(647\) 10.7329 3.48735i 0.421956 0.137102i −0.0903397 0.995911i \(-0.528795\pi\)
0.512295 + 0.858809i \(0.328795\pi\)
\(648\) 0 0
\(649\) −21.2912 −0.835754
\(650\) 0 0
\(651\) 9.28462 0.363893
\(652\) 0 0
\(653\) 34.0606 11.0669i 1.33289 0.433083i 0.445989 0.895038i \(-0.352852\pi\)
0.886903 + 0.461955i \(0.152852\pi\)
\(654\) 0 0
\(655\) −8.61248 + 15.6475i −0.336518 + 0.611397i
\(656\) 0 0
\(657\) 0.742534i 0.0289690i
\(658\) 0 0
\(659\) −32.1710 + 23.3736i −1.25320 + 0.910506i −0.998403 0.0564876i \(-0.982010\pi\)
−0.254801 + 0.966994i \(0.582010\pi\)
\(660\) 0 0
\(661\) 5.05420 + 3.67209i 0.196586 + 0.142828i 0.681724 0.731610i \(-0.261231\pi\)
−0.485138 + 0.874438i \(0.661231\pi\)
\(662\) 0 0
\(663\) −0.741109 1.02005i −0.0287823 0.0396154i
\(664\) 0 0
\(665\) 5.37202 + 2.95681i 0.208318 + 0.114660i
\(666\) 0 0
\(667\) −12.5486 4.07728i −0.485882 0.157873i
\(668\) 0 0
\(669\) −4.21398 + 12.9693i −0.162922 + 0.501422i
\(670\) 0 0
\(671\) −8.82193 27.1511i −0.340567 1.04816i
\(672\) 0 0
\(673\) −24.3712 + 33.5441i −0.939440 + 1.29303i 0.0166215 + 0.999862i \(0.494709\pi\)
−0.956061 + 0.293166i \(0.905291\pi\)
\(674\) 0 0
\(675\) −11.5844 + 7.33540i −0.445884 + 0.282340i
\(676\) 0 0
\(677\) 0.845914 1.16430i 0.0325111 0.0447477i −0.792452 0.609934i \(-0.791196\pi\)
0.824963 + 0.565187i \(0.191196\pi\)
\(678\) 0 0
\(679\) −9.34183 28.7512i −0.358507 1.10337i
\(680\) 0 0
\(681\) 1.72004 5.29373i 0.0659120 0.202856i
\(682\) 0 0
\(683\) 8.07088 + 2.62239i 0.308824 + 0.100343i 0.459329 0.888266i \(-0.348090\pi\)
−0.150505 + 0.988609i \(0.548090\pi\)
\(684\) 0 0
\(685\) 8.88027 + 18.8961i 0.339298 + 0.721984i
\(686\) 0 0
\(687\) 4.57827 + 6.30145i 0.174672 + 0.240415i
\(688\) 0 0
\(689\) 10.9745 + 7.97345i 0.418096 + 0.303764i
\(690\) 0 0
\(691\) −35.4186 + 25.7331i −1.34739 + 0.978933i −0.348248 + 0.937402i \(0.613223\pi\)
−0.999137 + 0.0415304i \(0.986777\pi\)
\(692\) 0 0
\(693\) 16.8456i 0.639910i
\(694\) 0 0
\(695\) −27.4078 29.2157i −1.03964 1.10821i
\(696\) 0 0
\(697\) −3.24510 + 1.05440i −0.122917 + 0.0399381i
\(698\) 0 0
\(699\) 10.6922 0.404418
\(700\) 0 0
\(701\) 0.840795 0.0317564 0.0158782 0.999874i \(-0.494946\pi\)
0.0158782 + 0.999874i \(0.494946\pi\)
\(702\) 0 0
\(703\) 3.28198 1.06638i 0.123782 0.0402192i
\(704\) 0 0
\(705\) 4.61311 2.16794i 0.173740 0.0816494i
\(706\) 0 0
\(707\) 28.3731i 1.06708i
\(708\) 0 0
\(709\) −10.8256 + 7.86529i −0.406566 + 0.295387i −0.772210 0.635367i \(-0.780849\pi\)
0.365644 + 0.930755i \(0.380849\pi\)
\(710\) 0 0
\(711\) 19.2401 + 13.9787i 0.721560 + 0.524244i
\(712\) 0 0
\(713\) −12.6025 17.3459i −0.471969 0.649610i
\(714\) 0 0
\(715\) −1.19914 + 6.26902i −0.0448453 + 0.234448i
\(716\) 0 0
\(717\) 2.99601 + 0.973461i 0.111888 + 0.0363546i
\(718\) 0 0
\(719\) 13.4159 41.2900i 0.500329 1.53986i −0.308154 0.951336i \(-0.599711\pi\)
0.808483 0.588519i \(-0.200289\pi\)
\(720\) 0 0
\(721\) 8.52195 + 26.2279i 0.317374 + 0.976776i
\(722\) 0 0
\(723\) −7.32076 + 10.0762i −0.272262 + 0.374737i
\(724\) 0 0
\(725\) 1.26405 19.7750i 0.0469458 0.734425i
\(726\) 0 0
\(727\) −18.8373 + 25.9274i −0.698639 + 0.961593i 0.301329 + 0.953520i \(0.402570\pi\)
−0.999967 + 0.00807318i \(0.997430\pi\)
\(728\) 0 0
\(729\) 4.81224 + 14.8106i 0.178231 + 0.548539i
\(730\) 0 0
\(731\) 2.06626 6.35930i 0.0764235 0.235207i
\(732\) 0 0
\(733\) 7.74091 + 2.51517i 0.285917 + 0.0929001i 0.448465 0.893801i \(-0.351971\pi\)
−0.162547 + 0.986701i \(0.551971\pi\)
\(734\) 0 0
\(735\) −2.33499 + 0.293788i −0.0861274 + 0.0108365i
\(736\) 0 0
\(737\) −12.5671 17.2971i −0.462914 0.637146i
\(738\) 0 0
\(739\) 5.76598 + 4.18923i 0.212105 + 0.154103i 0.688766 0.724984i \(-0.258153\pi\)
−0.476661 + 0.879087i \(0.658153\pi\)
\(740\) 0 0
\(741\) 0.495326 0.359876i 0.0181963 0.0132204i
\(742\) 0 0
\(743\) 21.9040i 0.803578i −0.915732 0.401789i \(-0.868388\pi\)
0.915732 0.401789i \(-0.131612\pi\)
\(744\) 0 0
\(745\) 13.8670 + 2.65248i 0.508048 + 0.0971795i
\(746\) 0 0
\(747\) −33.2953 + 10.8183i −1.21821 + 0.395820i
\(748\) 0 0
\(749\) −17.0877 −0.624373
\(750\) 0 0
\(751\) −9.21909 −0.336409 −0.168205 0.985752i \(-0.553797\pi\)
−0.168205 + 0.985752i \(0.553797\pi\)
\(752\) 0 0
\(753\) 4.92855 1.60138i 0.179606 0.0583577i
\(754\) 0 0
\(755\) −10.3651 1.98265i −0.377226 0.0721559i
\(756\) 0 0
\(757\) 45.6524i 1.65926i −0.558311 0.829632i \(-0.688550\pi\)
0.558311 0.829632i \(-0.311450\pi\)
\(758\) 0 0
\(759\) 2.55828 1.85870i 0.0928597 0.0674666i
\(760\) 0 0
\(761\) −32.2844 23.4560i −1.17031 0.850280i −0.179264 0.983801i \(-0.557372\pi\)
−0.991046 + 0.133521i \(0.957372\pi\)
\(762\) 0 0
\(763\) −18.0457 24.8378i −0.653299 0.899188i
\(764\) 0 0
\(765\) 11.4505 1.44070i 0.413994 0.0520886i
\(766\) 0 0
\(767\) −14.4499 4.69506i −0.521756 0.169529i
\(768\) 0 0
\(769\) 13.7024 42.1717i 0.494122 1.52075i −0.324198 0.945989i \(-0.605094\pi\)
0.818320 0.574762i \(-0.194906\pi\)
\(770\) 0 0
\(771\) −0.965710 2.97215i −0.0347792 0.107039i
\(772\) 0 0
\(773\) −22.6264 + 31.1426i −0.813816 + 1.12012i 0.176907 + 0.984228i \(0.443391\pi\)
−0.990723 + 0.135894i \(0.956609\pi\)
\(774\) 0 0
\(775\) 20.5498 24.7898i 0.738171 0.890476i
\(776\) 0 0
\(777\) −3.23733 + 4.45580i −0.116139 + 0.159851i
\(778\) 0 0
\(779\) −0.512006 1.57579i −0.0183445 0.0564586i
\(780\) 0 0
\(781\) 7.70061 23.7000i 0.275549 0.848054i
\(782\) 0 0
\(783\) 10.3361 + 3.35839i 0.369381 + 0.120019i
\(784\) 0 0
\(785\) 0.617158 3.22646i 0.0220273 0.115157i
\(786\) 0 0
\(787\) 31.1645 + 42.8942i 1.11089 + 1.52901i 0.820093 + 0.572231i \(0.193922\pi\)
0.290801 + 0.956784i \(0.406078\pi\)
\(788\) 0 0
\(789\) −10.4147 7.56674i −0.370774 0.269383i
\(790\) 0 0
\(791\) 26.3090 19.1146i 0.935440 0.679637i
\(792\) 0 0
\(793\) 20.3723i 0.723440i